Magical Resistance Rating (abbreviated MRR) is a form of damage mitigation was that introduced with Update 23.

It provides a percentage reduction in damage from acid, sonic, fire, electric, cold, alignment, light, positive, negative, poison, and rust. MRR is granted through multiple sources (items, feats, enhancements) and stacks with itself. Multiple effects granting an Enhancement bonus to Magical Resistance do not stack. Character sheets show the Magical Resistance Rating of the player next to the elemental resistances.

MRR is applied after resistances. MRR is applied to the damage that passes through the resistance and this is always rounded down. As such if a player would take 20 damage before resists or MRR was applied and had 10 resistance and 60 MRR (37.5% reduction), the result is:

Characters proficient with shields can also use the larger shields for defense against magical attacks that would normally require a Reflex saving throw. In addition to using your Reflex saving throw to mitigate the damage you can deflect the damage off your shield. This is represented by increasing your Physical and Magical Resist Ratings against those types of attacks when using a shield.

You gain this additional mitigation whether you make your Reflex saving throw or not.

Magical Resistance Rating (MRR) should work vs. traps and most other damage sources (not just spells). If you are wielding a heavy or tower shield, your MRR values are considered doubled against damage that can be halved with a Reflex save (whether traps or spells).